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Simplifying 72n4 + -168n2 + 98 = 0 Reorder the terms: 98 + -168n2 + 72n4 = 0 Solving 98 + -168n2 + 72n4 = 0 Solving for variable 'n'. Factor out the Greatest Common Factor (GCF), '2'. 2(49 + -84n2 + 36n4) = 0 Factor a trinomial. 2((7 + -6n2)(7 + -6n2)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(7 + -6n2)' equal to zero and attempt to solve: Simplifying 7 + -6n2 = 0 Solving 7 + -6n2 = 0 Move all terms containing n to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + -6n2 = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -6n2 = 0 + -7 -6n2 = 0 + -7 Combine like terms: 0 + -7 = -7 -6n2 = -7 Divide each side by '-6'. n2 = 1.166666667 Simplifying n2 = 1.166666667 Take the square root of each side: n = {-1.08012345, 1.08012345}Subproblem 2
Set the factor '(7 + -6n2)' equal to zero and attempt to solve: Simplifying 7 + -6n2 = 0 Solving 7 + -6n2 = 0 Move all terms containing n to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + -6n2 = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -6n2 = 0 + -7 -6n2 = 0 + -7 Combine like terms: 0 + -7 = -7 -6n2 = -7 Divide each side by '-6'. n2 = 1.166666667 Simplifying n2 = 1.166666667 Take the square root of each side: n = {-1.08012345, 1.08012345}Solution
n = {-1.08012345, 1.08012345, -1.08012345, 1.08012345}
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